The Clay Minerals Society Workshop Lectures Series, Vol. 21 (2016), Chapter 12, 151– 161
ON THE USE AND ABUSE OF N2 PHYSISORPTION
FOR THE CHARACTERIZATION OF THE
PORE STRUCTURE OF SHALES
PIETER BERTIER1, , KEVIN SCHWEINAR1, HELGE STANJEK1, AMIN
GHANIZADEH2, CHRISTOPHER R. CLARKSON2, ANDREAS BUSCH3,
NIKO KAMPMAN3, DIRK PRINZ4, ALEXANDRA AMANN-HILDENBRAND5,
BERNHARD M. KROOSS5, and VITALIY PIPICH6
1
Clay & Interface Mineralogy, RWTH-Aachen University, Bunsenstr. 8,
D-52072 Aachen, Germany
2
Department of Geoscience, University of Calgary, Calgary, Canada
3
Shell Global Solutions International, Kessler Park 1, 2288 GS Rijswijk,
The Netherlands
4
Dynchem, Saarstrasse 98, D-52062 Aachen, Germany
5
Institute for Petroleum & Coal, RWTH-Aachen University, Lochnerstr. 2,
D-52062 Aachen, Germany
6
Jülich Centre for Neutron Science JCNS, Forschungszentrum Jülich GmbH,
Outstation at MLZ, Lichtenbergstrasse 1 85747 Garching, Germany
e-mail: [email protected]
The use of N2 physisorption for the characterization of the pore structure of shales is
assessed by addressing some common pitfalls and misconceptions related to the
interpretation of physisorption data. In addition, N2 physisorption is compared to
other methods used to characterize shales. For this purpose a set of pore-structure
and total-porosity data from N2 physisorption, He-pycnometry, Hg-intrusion porosimetry, fluid saturation (Archimedes) methods, and (ultra) small-angle neutron scattering
was obtained from measurements on samples of Opalinus Clay.
1. Introduction
Porosity and pore structure are very important parameters in many geologic and engineering applications. With respect to shales and mudrocks, these properties are essential
in the assessment of multiphase transport, geomechanical behavior, and storage/sealing
capacity. Many methods are currently in use for the determination of porosity, each of
which has advantages and disadvantages. Though porosity is theoretically an intrinsic
property of a rock, different techniques often yield substantially different results.
This is certainly the case for shales, in which substantial micro- (,2 nm), meso(2 – 50 nm), as well as macro- (.50 nm) porosity is found. The lower range of pore
sizes, in particular, makes it difficult to characterize porosity adequately by routine
# Copyright 2016, The Clay Minerals Society
DOI: 10.1346/CMS-WLS-21.12
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methods such as those used for conventional reservoir rocks (e.g. petrography, X-ray
micro-tomography, Hg-intrusion porosimetry).
The increase in commercial production of shale hydrocarbons over the past decade
has resulted in a much-increased demand for porosity and pore-structure data for
shales. To meet that demand, the geoscience research community has adopted methods
from other disciplines which had proven useful in the characterization of micro- and
mesoporous materials. One of those is N2 physisorption analysis, a method which
relies on physical adsorption of nitrogen gas at liquid nitrogen temperature (77 K).
Adsorbed amounts of gas are measured (volumetrically or gravimetrically) as a function
of relative pressure (absolute/saturation pressure). The resulting isotherms reflect
mechanisms of pore filling, the physics of which can be used to infer pore volume
and area distributions. N2 physisorption analysis is an attractive method for characterizing shales because it is commercially available, inexpensive, and comes with commercial data-processing software which produces a myriad of information about the pore
system of the samples being analyzed. The method was originally developed for
applications in material sciences and physical chemistry (ceramics, catalysts, separation
technology, pharmaceuticals, etc.). Substantial progress has been made recently in the
interpretation of gas physisorption isotherms due to the development of novel engineered nanomaterials (reviewed by Thommes and Cychosz, 2014). These are ideal standards for characterizing physisorption mechanisms, because their pore structure is
homogeneous and ordered, which allows for accurate quantitative assessment by
diffraction methods.
CO2 physisorption analysis is commonly used for characterization of micropores and
is complementary to the N2 method. Ar physisorption (at 87 K) has certain advantages
over N2 (Thommes and Cychosz, 2014), but to date it has not been applied much in shale
characterization. These techniques will not be addressed further here.
2. Principles of N2 physisorption
When nitrogen gas is in contact with a solid at 77 K, a specific number of gas molecules
will be attracted to the surface of the solid by van der Waals forces (Thommes and
Cychosz, 2014). This process is known as physical adsorption or physisorption. The
interaction energy of physisorption is low, which distinguishes it from chemisorption
(Rouquerol et al., 2014). Physisorption is thermodynamically reversible at isothermal
conditions, which is not the case for chemisorption. Chemisorption is insignificant in
the case of N2 on shales and so is not considered further here.
The number of physisorbed molecules depends on the relative pressure of the N2 gas
in equilibrium with it. Relative pressure ( p/p0) is the ratio of absolute gas pressure to
saturation pressure, i.e. the pressure at which the unconfined gas condenses. The saturation pressure of N2 at 77 K is 101.3 kPa because 77 K is the boiling point of N2. At a
given relative pressure, the amount of gas at a specific part of the surface of a solid
depends on local surface-energetic properties and on the geometry of the surface.
To interpret physisorption measurements of porous systems, surfaces are classically
On the use and abuse of N2 physisorption
153
assumed to be homogeneous, so the amount adsorbed at a specific relative pressure is
determined by pore size/geometry. These two aspects are clearly intimately related,
so assumptions have to be made about geometry to obtain pore size. The most
common assumption is that of a cylindrical pore system. At low pressures ( p/p0
,0.2), micropores are filled with N2; as pressure increases mesopores fill; and from
p/p0 ¼ 0.96, macropores are filled. Theoretically, at p/p0 ¼ 1 all pores are filled,
but in practice this implies that the free space in the measurement cell is filled with
N2, so high relative pressures yield no relevant information (Rouquerol et al., 2014).
Specific relative pressure ranges are associated with specific adsorption mechanisms.
Desorption of N2 occurs partly by different mechanisms. Physical models of these
adsorption and desorption mechanisms constitute the basis for the interpretation of
isotherms in terms of porosity and pore structure.
3. Data-processing methods and their applicability
to shale samples
N2 physisorption isotherms hold a wealth of information about surface area and energy;
only the theories used for the extraction of porosity and pore structure of shales will be
addressed here.
The simplest way to extract porosity information from N2 isotherms is by use of Gurvich’s rule (Rouquerol et al., 2014) which states that the amount adsorbed at the limiting
plateau of an isotherm is a measure of the total adsorption capacity, and to obtain the
corresponding total pore volume, the adsorbate can be assumed to have the molar
volume of the liquid at the operational temperature. Gurvich’s rule was developed for
mesoporous materials (Gurvich, 1915), restricting its applicability for micro- and
macroporous materials such as shales. The presence of micropores results in inaccurate
total pore volumes because of molecular sieving by smaller micropores and deviations from the liquid density in micropores (positive or negative, depending on the
material) (Thommes, 2010). Isotherms of macroporous materials do not have limiting
plateaus corresponding to the maximum adsorption capacity. The isotherms increase
asymptotically toward p/p0 ¼ 1, which makes the Gurvich total pore volume very
sensitive to the choice of the relative pressure point. This can be overcome pragmatically by assigning a pore diameter to the selected relative pressure (e.g. by use of
the Kelvin equation), and reporting it together with the ‘total’ pore volume. Several
papers on shales report Gurvich pore volumes for pore diameters below 0.35 mm,
corresponding to a relative pressure of 0.995 (e.g. Rexer et al., 2013; Mastalerz
et al., 2013; Chen et al., 2014; Liu et al., 2015; Cao et al., 2015). The reported pore
volumes are specific, i.e. in cm3/g, while porosity is generally desired as a volume
fraction. This implies that an extra measurement of grain density is required for
which He-pycnometry data can be used, or a value calculated from the mineral composition of the sample, if available.
The Barrett-Joyner-Halenda (BJH, Barrett et al., 1951) method is used widely to calculate the pore-volume (and area) size distribution (PSD, i.e. the pore volume or surface
154
P. Bertier et al.
area associated with each pore size range) of shales. This method relies on the Kelvin
equation which describes the effect of surface curvature of a liquid – vapor meniscus
on the vapor pressure and thus relates pore diameter to relative pressure. For practical
use in N2 physisorption, unconnected cylindrical pore geometry is assumed, so the
resulting PSD represents an equivalent capillary bundle, analogous to mercury intrusion
porosimetry. Because the Kelvin equation describes capillary condensation phenomena,
its relevance is restricted to the relative pressure range where those occur, i.e. to mesoand smaller macropores. The Kelvin radius is the radius of a meniscus, not the pore
radius, because pore walls are lined with layer(s) of adsorbate before capillary condensation occurs. The BJH radius is, therefore, the sum of the Kelvin radius and the statistical thickness of the adsorbate layer. For smaller mesopores during adsorption, in
particular, this statistical thickness (t) contributes substantially to the BJH radius.
Several models are used to calculate t and these are based on measurements of nonporous reference materials and theoretical considerations. The Harkins-Jura equation,
based on Al2O3 (Harkins and Jura, 1944), has been suggested to be appropriate for
analysis of shales (Kuila and Prasad, 2013). Comparison based on an extensive shale
data set showed that the choice of the t model does not make a significant difference
if the BJH theory is applied within the p/p0 where it is valid.
The range of validity of the BJH theory is a crucial issue, which, all too often, is
ignored or misconceived by researchers working with shales. Firstly, adsorption and
desorption in mesoporous materials such as shales, happen by different mechanisms.
This is shown by pronounced hysteresis of the N2 isotherms at p/p0 . 0.42. During
adsorption, pores fill gradually by molecules adsorbing in layers of increasing thickness
on pore walls. In the course of desorption, the same pores empty by withdrawing
menisci at the gas – liquid interface. This is an oversimplification, but it illustrates
the concepts. Both isotherm branches can be used to obtain BJH PSD, but they yield
different information. Research on engineered materials containing spherical pores
with cylindrical throats, for example, showed that desorption is determined by
throats, while adsorption holds information on the pore bodies (Thommes, 2010). For
complex systems of pores, covering broad ranges of diameters and shapes, randomly
organized in networks as in shales, the explanation of the difference between adsorption
and desorption data is less trivial but must be considered in the interpretation of the PSD.
The menisci controlling desorption become unstable at p/p0 ¼ 0.42 for N2 at 77 K.
This is classically considered as an inherent property of the fluid (and T, the ‘tensile
strength effect,’ Groen et al., 2003) but was recently shown to depend to some extent
on pore size (Thommes et al., 2006; Rasmussen et al., 2010). The forced closure of
the hysteresis loop at p/p0 ¼ 0.42 produces an artefact in BJH PSD, i.e. a spike or
steep slope at 3.8 nm in differential and cumulative distributions, respectively. This
artefact makes up a substantial part of the pore volume of shales. Though this is well
established, recent papers on shales often interpret it as a rock property (e.g. Olabode
and Radonjic, 2014; Cao et al., 2015; Tang et al., 2015). Adsorption data are not affected
by this artefact, but are subject to other issues. Studies on engineered materials showed
that BJH underestimates the pore size by up to 20– 30% for mesopores which are
,10 nm in size (Thommes, 2004).
On the use and abuse of N2 physisorption
155
The most advanced and accurate methods to analyze pore structures from physisorption data are based on density functional theory (DFT) or Monte Carlo simulations of
molecular dynamics (MC) (for reviews, see Thommes, 2010 or Rouquerol et al.,
2014). The DFT or MC is used to calculate the pressure dependency of density profiles
for N2 confined in pores with specific geometries in specific solids. This enables calculation of reference isotherms for specific pore systems. By varying pore-size parameters,
these calculated isotherms are fitted iteratively to measured data. This procedure was
shown to produce excellent results for engineered materials. For those, pore-size and
geometry parameters can be constrained sufficiently to obtain unique fits. For compositionally heterogeneous materials with complex pore systems, such as shales, this is not
the case. Experimental data can be fitted perfectly, but the results are unreliable. At
present, none of the available kernels (gas-solid-geometry models) is suitable for
(organic-rich) shales. Despite warnings from developers against application of their
kernels for systems other than those for which they were designed, many geoscientists
seem to interpret the numbers produced without much consideration. Fortunately, new
and more complex kernels are being released at an increasing pace, and it is likely that in
the near future DFT-MC models suitable for shale analysis will be developed.
4. The conundrum of low-pressure hysteresis
Several recent physisorption studies on shales report N2 isotherms displaying a hysteresis at p/p0, 0.42, but none has addressed it specifically in adequate detail (e.g. Kuila
and Prasad, 2013; Mastalerz et al., 2013; Chen and Xiao, 2014; Cao et al., 2015). Handbooks are quite clear about low-pressure hysteresis (LPH): any hysteresis below this
pressure violates the thermodynamics of equilibrium physisorption, and should,
therefore, be related to chemisorption, structural deformation of the sample, or lack
of thermodynamic equilibrium (Rouquerol et al., 2014). In all of those cases, physisorption-based theories are invalid. Systematic analyses of the present shale sample set
showed that this LPH is most common for mature black shales, and is perfectly reproducible. The latter implies that chemisorption and deformation can be excluded.
The lack of an equilibrium hypothesis was tested and confirmed by systematic physisorption measurements with different equilibration times, on a shale sample (200 –
400 mm particle-size fraction) showing substantial LPH (Figure 1a). N2 physisorption
isotherms were measured with different equilibration criteria. Equilibrium was
assumed when the pressure change per equilibration time interval was ,0.01% of the
average pressure during this interval. Equilibration time intervals were between 10
and 60 s (total isotherm measurement times ¼ 8– 40 h). These results show that even
at very long equilibration times the hysteresis loop does not close at low pressures.
Longer equilibration times resulted in larger amounts adsorbed for both the adsorption
and desorption branches over the entire relative pressure range. For one isotherm
(Figure 1a: orange, 20 s equilibration time) 50 closely spaced data points between
0.30 and 0.31 were recorded during adsorption and desorption, which implies that the
sample was kept at relatively constant pressure for 7 h during adsorption and 4 h
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P. Bertier et al.
a
Equilibration time = 10 s
Equilibration time = 20 s
Equilibration time = 20 s, step 0.30–0.31
Equilibration time = 30 s
Equilibration time = 60 s
Quantity adsorbed (mmol/g)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Relative pressure (P/P0)
b
0.20
Quantity adsorbed (mmol/g)
P/P0 = 0.95, CD = 1.1e-12 m2/s
0.15
0.10
P/P0 = 0.30, D = 1.0e-14 m2/s
0.05
P/P0 = 0.02, D = 5e-14 m2/s
0.00
0
200
400
600
800 1000
Measurement time (min)
Figure 1. (a) N2 physisorption isotherms of a shale sample (200–400 mm fraction), displaying substantial
low-pressure hysteresis, measured with different equilibration criteria. Equilibration time intervals were
between 10 and 60 s (total isotherm measurement times: 8 –40 h). These results show that even at very
long equilibration times the hysteresis loop does not close at low pressures which confirms that shale
samples displaying low-pressure hysteresis do not attain sorption equilibrium during measurement.
(b) Amount adsorbed as a function of time, measured (circles) at constant relative pressure, on the aliquot
of shale from Figure 1a. The lines are fits to the data points, of the analytical solution of Fick’s Law (100
summation terms), for diffusion into a sphere (r ¼ 150 mm), for which the effective diffusion coefficients
(D) obtained are displayed. The low values for D over the entire relative pressure ranges suggest strong
diffusion control on the adsorption process.
On the use and abuse of N2 physisorption
157
during desorption. The adsorption branch shows a pronounced step in this p/p0 range,
while desorption is unaffected. These findings confirm that shale samples displaying
LPH do not attain sorption equilibrium within reasonable measurement times.
The amount of N2 adsorbed is very time dependent for samples displaying LPH. The
relation between amount adsorbed at constant relative pressure and time was fitted by
Fick’s second law for diffusion into a sphere (Crank, 1975), yielding low, but reasonable, effective diffusion coefficients (10214 – 10212 m2/s) for N2 in shales at 77 K
(Figure 1b).
These results imply that either a substantial amount of pore volume is present in ultramicropores in which N2 diffusion is very slow, or that part of the pore volume is only
accessible through very small such pores. In practice this implies that the pore
volume of shales displaying LPH could be substantially underestimated.
5. Comparison of results from N2 physisorption with those
from other methods
5.1. Materials and methods
Porosity and PSD results from N2 physisorption were compared with results from
He-pycnometry, Hg-intrusion porosimetry, water saturation, and small-angle neutron
scattering for a set of nine samples of Opalinus Clay (Figure 2). These were taken
from a 2 m section of homogeneous core from the Mont Terri laboratory (Switzerland).
Mineral quantification was performed by Rietveld refinement, using the Profex-BGMN
software (Doebelin and Kleeberg, 2015), of X-ray diffraction (Huber MC9300, HUBER
Diffraktionstechnik GmbH & Co. KG, Rimsting, Germany) patterns recorded on randomly oriented bulk samples. X-ray fluorescence spectrometry (Spectro XLab2000,
SPECTRO Analytical Instruments GmbH, Kleve, Germany) was used for bulk chemical
analysis of the major and minor elemental compositions. In addition, the cationexchange capacities of the samples were measured by photospectrometric determination
of the CuTrien uptake of crushed samples in suspension. Details of these characterization methods and data were given by Amann-Hildenbrand et al. (2015). Mineralogical
and chemical analysis confirmed the low heterogeneity of the sample set.
He-pycnometry, Hg-intrusion, and water-saturation methodologies were listed by
Amann-Hildenbrand et al. (2015); small angle neutron scattering (SANS) measurement
conditions were identical to those of Kampman et al. (2016). The pore-size ranges of the
applied methods accessed are summarized in Figure 2.
N2 physisorption analysis was performed using a Micromeritics Gemini VII 2390t
device (Micromeritics Instrument Corporation, Norcross, Georgia, USA), by means
of the static volumetric method, in a liquid N2 bath. A crushed fraction of 63–
400 mm, prepared manually in a mortar with minimal use of energy to avoid strain,
was measured. The samples were outgassed at 1308C below 3 Pa for .24 h. Adsorption
was measured at 42 relative pressure steps between 0.001 and 0.995 and desorption at 29
relative pressure points between 0.995 and 0.1. The nitrogen saturation pressure ( p0)
158
30
(U)SANS
He-pycnometry
25
N2 physisorption
19.4
1.5 nm
Hg-intrusion uncorrected
~1 nm
0.18 nm
12.8
10-7
10
2 nm
10.2
10-5
Micro
10-4
Methods used
in this study
45 μm
0.18 μm
50 nm
Meso
10
10-3
~6 μm
(U)SANS
N2 Physisorption
11.6
10-6
He Pycnometry
Archimedes
Mercury Intrusion Porosimetry
~0.15 nm
Hg-intrusion corrected
15
10
-8
IUPAC Pore
Classification
Macro
40 nm 400 nm
Transition/Knudsen
Slip
5
Atoms/
molecules
1Å
0
1 nm
Gas Flow
Continuum/Darcy
2 μm
63 μm
Clay
Silt
1 μm
Particle Size
Sand
1 mm
Opalinus clay
Figure 2. Comparison of the average porosities (vol.%, +2 standard deviations) of nine Opalinus Clay samples (Mont Terri, Switzerland) measured by combined
Small-angle neutron scattering– ultra-small-angle neutron scattering (SANS-USANS), He-pycnometry, Archimedes’ method (water saturation), N2 physisorption
(Gurvich pore volume, max. pore diameter ¼ 0.35 mm), and Hg-intrusion porosimetry (with or without correction for surface roughness, see AmannHildenbrand et al., 2015). These samples were taken from a 2 m long, homogeneous section of core. The mineralogy and chemical composition were presented
by Amann-Hildenbrand et al. (2015).
P. Bertier et al.
Porosity (%)
10
-9
Archimedes, water
20.8
20.1
20
Pore radius c/(m)
-10
On the use and abuse of N2 physisorption
159
was determined separately for each relative pressure point. Sorbate-sorbent equilibrium
was assumed when the pressure change over a 10 s interval was ,0.01% of the average
pressure during the latter interval. Gurvich pore volumes were calculated from the p/p0
point at 0.995 (BJH diameter of 0.35 mm) assuming liquid nitrogen density
(28.8 mol/L). Porosities were calculated from specific pore volumes using the grain
density from He-pycnometry.
6. Results
The average porosity of the nine samples studied, and its variability over the sample set,
are summarized in Figure 2, for each of the porosimetric techniques applied. The results
of N2 porosity data are between 40 and 60% of the He-pycnometry values. Helium, as a
very small molecule with low affinity for solids, is likely to access all pores during
pycnometry, which is not the case for N2. Water saturation yielded porosities similar
to He-pycnometry for samples saturated under confinement in a triaxial cell. The
samples studied contain swelling clays (illite-smectite mixed-layer clays) but have
small cation exchange capacities (150 mmol/g). No substantial swelling due to water
saturation was observed. Total porosity values from Hg-porosimetry are smaller than
the N2 data for all samples, though the method accesses a broader range of pore sizes
(1.5 nm– 45 mm). This might be due to compression of the samples at the high isotropic
pressure applied during measurement (Clarkson et al., 2013). (U)SANS data, covering a
pore-size range of 2 nm to 10 mm, correspond well to He-pycnometry. Pore-size distribution data from neutron scattering are in fair agreement with those from N2, while
Hg-intrusion gave very different PSD values, in the pore-size range of overlap.
This unique data set of shale porosities from different measurement techniques shows
clearly that although the individual techniques are reasonably precise, the accuracy of
porosity measurements is problematic. The inaccuracy is related partly to the different
pore-size ranges assessed by the specific methods, yet this does not explain all of the
differences quantitatively.
7. Summary and conclusions
N2 physisorption is a useful technique in the analysis of the pore structure of shales and
mudrocks, but the results should be interpreted with caution:
(1) Gurvich total pore volumes do not represent the total porosity of shales because
N2 physisorption does not yield information about pores larger than 0.35 mm
and the density of N2 in micropores differs from that of liquid N2 at 77 K.
(2) Barrett-Joyner-Halenda (BJH) pore-size distributions from desorption isotherms
represent pore-throat sizes and should not be used for pores smaller than 4 nm,
due to artefacts related to the forced closure of capillary hysteresis loops. Poresize distributions from adsorption isotherms give information about pore bodies.
BJH data underestimate substantially the volumes of pores of ,10 nm in size.
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(4)
P. Bertier et al.
Low-pressure hysteresis observed mainly for organic-rich shales is related to
incomplete equilibration during measurements, due to slow diffusion in small
micropores and restricted access to significant fractions of pore volume through
micropores. Inversion of isotherms displaying low-pressure hysteresis gives
inaccurate information on pore structures.
Gurvich pore volumes for pores smaller than 0.35 mm, calculated from N2 physisorption on a set of Opalinus Clay samples, correspond to 40– 60% of the values
of porosity from He-pycnometry, neutron scattering, and water saturation.
Hg-intrusion total porosities are lower than N2 physisorption values. Pore-size
distributions using BJH correspond fairly well to those from neutron scattering,
but differ substantially from Hg-intrusion.
Acknowledgments
Guest editor: Reiner Dohrmann
The authors and editors are grateful to anonymous reviewers who offered very helpful
input and suggestions. A list of all reviewers is given at the end of the Preface for this
volume.
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